You pay only were you live and work. I would speak with your firm or an account. Your LLC might have to pay tax in NYC since you are a partner though.

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When it comes to the very greedy New York State the tax laws are not so simple. From the New York Times:

Telecommuters Not Exempt From New York Tax

By MICHAEL COOPER

Published: March 30, 2005

LBANY, March 29 - Commuters from out of state who take cars, trains and buses to jobs in New York have long grumbled about having to pay New York State income tax. A ruling handed down on Tuesday by the state's highest court found that the growing ranks of telecommuters from out of state must also pay.

The Court of Appeals ruled 4 to 3 that a computer programmer for a group of trade unions in Queens who works mostly out of his home in Nashville must pay New York State tax on all his income, not just on part.